Residual stresses in polycrystals as influenced by grain shape and texture

Abstract R esidual stresses in polycrystals arise because of anisotropic thermal expansion of constituent crystals. Due to the random crystal arrangement, the internal stresses also become random quantities, which have to be described by probability distributions or statistical moments. Conditional first order moments (averages) and second order moments (fluctuations) can be derived if the elastic energy stored in the residual stress field is known. By applying the Green function method, an analytical expression for this energy is obtained under some mild assumptions concerning the neglected elastic anisotropy and crystallographic correlations between the crystals. From the stored energy we calculate the average crystal stresses as depending on shape, orientation and polycrystalline texture. Furthermore we obtain a scalar second order moment of the residual stress, which also depends on grain shape and texture. The results arc evaluated for alumina ceramics and zircalloy.

[1]  N. Laws,et al.  Microcracking in polycrystalline ceramics: elastic isotropy and thermal anisotropy , 1989 .

[2]  Anthony G. Evans,et al.  Some effects of microcracks on the mechanical properties of brittle solids—I. Stress, strain relations , 1985 .

[3]  D. Clarke.  Microfracture in brittle solids resulting from anisotropic shape changes , 1980 .

[4]  W. Kreher,et al.  Residual stresses and stored elastic energy of composites and polycrystals , 1990 .

[5]  A. Evans.  Microfracture from thermal expansion anisotropy—I. Single phase systems , 1978 .

[6]  Rudolf Zeller,et al.  Elastic Constants of Polycrystals , 1973 .

[7]  W. Kreher.  Internal stresses and relations between effective thermoelastic properties of stochastic solids - some exact solutions , 1988 .

[8]  C. Kleint,et al.  X-Ray Diffraction and Conductivity Investigations of Lanthanum-Doped Barium Titanate Ceramics , 1989, September 16.

[9]  J. B. Wachtman,et al.  Elastic Constants of Synthetic Single‐Crystal Corundum at Room Temperature , 1960 .

[10]  H. Wenk.  Preferred orientation in deformed metals and rocks : an introduction to modern texture analysis , 1985 .

[11]  R. Hill.  Elastic properties of reinforced solids: some theoretical principles , 1963 .

[12]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[13]  M. Ortiz,et al.  Microstructural thermal stresses in ceramic materials , 1988 .

[14]  S. Ahzi,et al.  A self consistent approach of the large deformation polycrystal viscoplasticity , 1987 .

[15]  R. Hill,et al.  On macroscopic effects of heterogeneity in elastoplastic media at finite strain , 1984, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  E. Kroner.  Self-consistent scheme and graded disorder in polycrystal elasticity , 1978 .

[17]  S. Macewen,et al.  The influence of prior deformation on hydride precipitation in zircaloy , 1992 .

[18]  J. Hutchinson,et al.  Microcracking in Ceramics Induced by Thermal Expansion or Elastic Anisotropy , 1988 .

[19]  S. Macewen,et al.  Residual stresses in annealed zircaloy , 1989 .